Circle Review and Chords

Circle Review and Chords

Pre
-
Calculus 30S


A. Objectives



Cognitive Domain:

The student will learn that the perpendicular bisector of a chord contains the centre
of a circle and an inscribed angle is twice the measure of a central angle. The
student will

also learn that previous information about circles and geometry will be
combined to learn the new material. The student will also learn that proving
theorems requires using other theorems they have seen previously.


Psychomotor Domain:

The student will d
emonstrate a basic knowledge of parts of circles and the two new
theorems by playing matching game, working through a work sheet, doing some
paper folding, taking notes and participating in the class and with each other.


Affective Domain:

The student will

value the skill/ability of remembering circle parts and being able to
find the centre of a circle and its applications. The student will value the ability to
prove geometric theorems.


B.

Introduction (2
-
3 min.)


Topic: Review of circle parts and introduce

chords and angles


Statement: “Today, we'll be starting a new unit on circle geometry. We'll begin by doing a
little bit of review and then jump into new material. The first three exercises of this unit will
be tested on Friday, so we are going to have

to work hard to get everything done.”


C.

Body (85 min.)

1.

Mental Math (8 min.)

2.

Investigation 1 (10 min.)

-
do questions #1
-
4

-
discuss the result and tangent lines

3.

Matching game and definitions (20 min.)

-
use the following words:

tanget

circle


chord


diameter

radius


central angle

H
-
L

SAS


ASA


bisect


arc


inscribed angle

supplementary


perpendicular

congruent

complimentary

-
see attached sheet for the definitions to give for notes

4.

Investigation 2 (15
-
20 min.)

-
do question #6 with table partners

-
do the notes

(give theorem, prove, example)

-
theorem: the perpendicular from the centre of a circle to a chord bisects the chords (and
vice versa)

5.

Investigation 3 (15
-
20 min.)

-
do question #7 with table partners

-
do the notes (give theorem, prove, exmaple)

-
theorem:

the measure of the central angle is equal to twice the measure of the inscribed
angle subtended by the same arc

6.

Assignment and work time (rest of class)

-
assign 27 (we did #1 already)


D. Conclusion (1
-
2 min.)


Summary: “We did a really quick review to
day of different circle parts and theorems in
geometry you've seen before. We added a couple of new theorems and modelled how to go
about proving them.”


Assignment: Exercise 27 (except #1)


Evaluation



Student:

Did the students show an understanding o
f the material?

Did the paper folding and drawing help the students to visualize the new
theorems?

Did the students remember a lot of the theorems and circle parts that they
had learned previously?



Teacher:

Did I show an understanding of the material?

Wa
s I clear and consice in my explanations?

Did I handle the transitions well between all the different activities?


E. Teaching Aids

-
overhead and overhead pens

-
investigation sheet (for students)

-
sheet with different sized circles (for students and overh
ead)

-
paper folding circles

-
ruler, compass and protractor

-
notes/example sheet


F. Timing


Included within the introduction, body and conclusion.